# Re: [ocio-dev] Digest for ocio-dev@googlegroups.com - 2 updates in 1 topic

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### Joseph Goldstone

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Jul 19, 2018, 1:07:08 PM7/19/18
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Pretty sure there was a killer typo in Guarav’s illustration of tetrahedral interpolation though. There was supposed to be a second edition of that book (“Digital Color Imaging Handbook”, not “Digital Color Handbook”), and Amazon still shows a mock-up page for it, but it never came out.

To ARRI Partner Program members who are curious about this we recommend one of Kang’s books. You could look at pp. 70-72 of “Color Technology for Electronic Imaging Devices":
https://books.google.com/books?id=vzQH3qA_RKkC&pg=PA72&lpg=PA72&dq=kang+tetrahedral+interpolation&source=bl&ots=DC1eh_t_Xh&sig=3DrpvVzNk2RaTz3fZV7c32Wm2Hw&hl=en&sa=X&ved=0ahUKEwjql8_iz6vcAhUNKXwKHfneA8cQ6AEIVzAG#v=onepage&q=kang tetrahedral interpolation&f=false

But there’s also the Truelight documentation, and Richard Kirk does a nicer, I think, job of presentation than Kang (perhaps because Richard only outlines one scheme, whereas Henry Kang seems to outline every conceivable interpolation scheme ever invented). If you go to this page:
and download the "Truelight Software Library” document from 2006, § 6.6 (“Colour Cube Transforms”), pp. 55-57, does a nice job and includes straightforward C code. I haven’t personally tested the code by cutting and pasting but I suspect it works. You want to be sure that the tetrahedra are cut in such a way that the (0,0,0) to (1,1,1) chord of the cube runs along tetrahedral edges — this is kind of the natural way to do it, and in fact is how the (probably little used) 3D LUT processors in the original DLP Projector electronics packages did it, back in the day — a handy thing back when image processing components were twenty years behind today’s components in terms of performance.

On Jul 18, 2018, at 1:35 PM, ocio...@googlegroups.com wrote:

 michael...@gmail.com: Jul 17 11:04PM -0700  I guess this means that the lut processor doesn't use (256 256 256)  nomenclature when it outputs a color, so it doesn't have to perform a  conversion to (256 256 256) by multiplying by 63. That would make sense,  since it would be faster. And as for interpolation, I think we were both  referring to the same 2x2x2 cubes. You said ({6|7}, {12|13}, {18|19}),  while I used cartesian coordinates. Your way of expressing it makes sense  and fills in the blanks for me.   So I think I've got it, and thank you very much! How did you learn this  stuff? I can't find even one book that explains the math of cube luts. Can  you recommend any books or journal articles? My search has been  frustrating, as I said before, and I feel very fortunate that you've helped  me out. Anything you recommend I will definitely read.   Try it yourself, do a search and see if you can find any technical  documentation. Maybe I just don't know the right keywords. But I have a  feeling that other people who are curious about luts are going to find this  conversation in the future, and it will be a good resource for them too.       On Tuesday, July 17, 2018 at 12:11:42 AM UTC-4, Dennis Adams wrote: Jim Houston : Jul 18 12:07AM -0700  > On Jul 17, 2018, at 11:04 PM, michael...@gmail.com wrote:   > I can't find even one book that explains the math of cube luts.   One source is Chapter 11 of Digital Color Handbook by Guarav Sharma, CRC Press 2003 — “Efficient Color Transformationion Implementation”   Jim Houston
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